Lord Varys,
I am not going to answer you point by point because this conversation is circular and each point-by-point ends up having to be longer and longer to wade through everything.
Your basic argument from what I can tell, is that the show must have invented something that does not even bear the slightest resemblance to where the books will go, because seeing it as an adaptation does not fit with your various theories and understanding of the political context of the books.
My basic argument is that the show's adaptation is largely working around the absence of Aegon, which necessarily means that things play out rather differently. However a Lannister power grab is simply too key a moment for it to be pure invention for the show IMO, in spite of any differences in the form it will take in the books. And in fact the books have established several details that make it far more likely a possibility than you are admitting.
I am not inventing the level of investment that various players have in Lannister power. We learned from the very first book the extent to which the Lannisters had infiltrated everything. We also learned just how many land grabs the Lannisters had made via various marriages and deal making during the war. What that level of stakes in Lannister power means is that people who are now dependent on Lannister patronage are far less concerned about Cersei having been shamed and having a weak claim etc. than they are about losing what they have gained from patronage.
There are certainly many people who are NOT invested in Lannister rule in the Kingdoms, however those people are already preparing for war, whether Tommen is still King or Cersei makes a move to replace him. Cersei making a power grab will not affect them because they are already enemies.
Meanwhile, the Reach is under attack. The Stormlands have fallen to Aegon. Tyrell forces took heavy losses at Dragonstone. You talk as if the Tyrell army is unlimited and has nothing to do but hang out in KL. But that is simply not true. And for their part, an alliance with the Sparrows is not that huge a stretch either, given the emphasis the books have given to Margaery's frequent sept visits, charity, and shows of piety.
In short then, the show's version is a version, not an invention, and it is a version based on trying to get to more or less the same place without Aegon in the picture.

1. The Tyrell forces, more specifically Tarly, are already invested in the Riverlands and Crownlands, and generally the aftermath of the Northern war. So much so that Dickon even married a Mooton. The Freys are about to descend into a heredity dispute leaving a power vacuum, and the only somewhat capable army on the ground there is a band of religious knights under Hasty aside from the Lannisters. Tarly only left because of Margaery's arrest, but he is a prideful man, and what he was trying to accomplish in the region was not accomplished; the BWB still operate freely, and the region is not subdued.
2. The Faith Militant are not a threat to the Tyrells if the Tyrells ally with them, which they would do because the alliance with the Lannisters is in trouble and they want to hold power. There is no reason at all to assume what happened in the show with Margaery was anything other than an ADAPTATION of future events in the books. Different, yes, but leading in essentially the same direction, which is for the Tyrells to adapt to and make use of the Sparrow situation. Once Margaery's trial is over the Sparrows are a threat to Cersei, not to them.
2b. Aegon is not their only problem. The Reach itself had been invaded at the point we left off. They may have a large army, but they are also being forced to fight on several fronts.
3. Slynt has not been in charge of the city watch for a long time. Humphrey Waters is the latest commander, and his appointment took place while Kevan was running things. Regardless of the commander, the watch itself has been weighted Lannister for a very long time and the addition of a hundred Tyrells recently will not change the balance all that much.
4. Just because you don't like the way the show did it it seems, does not at all mean that GRRM will not write a version that, with the addition of a few more power moves and details, will not make sense. Yes, Cersei was brought low by the walk. That does not at all change the extent to which the power structures of the Realm have become invested over the course of Robert's reign and beyond, in Lannister patronage, and how they therefore have no interest in seeing the Lannisters thrown out.

^There is a Tyrell army there for now, yes.
However, some have been sent back to the Reach to defend it from Euron. Some will be sent to the Stormlands fight Aegon. And some are still needed in the Riverlands as rebellions are far from over.
The Lannister forces are not decimated, they are still very capable of being a threat, and meanwhile, over the years, nearly every important position in the administration of the Realm has been filled with Lannister sympathizers who have far too much stake in the current order to ever let the Lannisters lose power. This includes the KL city watch. So when Tommen dies, Cersei is their only real option for maintaining their position.
A coup in the books is therefore very much possible, it will simply be a more complicated scenario and will unfold quite differently.

I tend to agree things in the books will play out very very differently, but disagree that the result won't be similar, with Cersei claiming the throne.
The main difference is certain to be Aegon and how he fits into the picture.
In the books, Tommen is much younger. He definitely likes Marge a lot, but he is too young to get heart sick and jump out of the window. There is also the fact that Tyene in the books will be infiltrating the Sparrows.
I think the way things play out in the books, Tommen will be murdered. The Tyrells will jump to Aegon, and Cersei will claim the throne as the city faces invasion. She will then possibly burn the city to kill the invaders, which is what Aerys actually wanted to do to Tywin's army.

you are being truly, truly naive.
Why on earth would ANYONE, in the current instability, patiently sit around for the months and months that would take, in a time of brewing war, in order to let a bunch of maesters decide their fates for them?
You don't get it. SOMEONE was going to simply take that throne in that situation, and Cersei was simply the one to do it. She is the closest remaining relative of the dead King (officially still fathered by Robert), and as such, has as much grounds to do so as anyone else, but the most important factor is that she simply did it.
Yes, her legal claim is weak, but there is simply noone around with any stronger claim in the Kingdoms that remain invested in the Baratheon dynasty. EVERYONE's claim is weak, and power vacuums are disastrous for everyone.
Furthermore, there is not a single person in the Kingdoms who is not aware that Robert's reign and beyond was backed in every way by the Lannisters, and that they were the true power behind the throne. The Lannister backing existed because of Cersei's marriage to Robert, and now that the Baratheons are gone, maintaining the illusion of continuity rests on maintaining the power structure as is, which is heavily weighted Lannister. There is noone else who can maintain that sense of continuity. Everyone else is in fact even more of a conqueror because their reign would imply dismantling that Lannister power structure and replacing it with a major unknown. The people who want that are already enemies and are backing Dany or Jon. The remaining people have major stakes in the current order and are NOT interested in seeing it uprooted.

There are frankly no options without some kind of serious hurdle. Jon was just declared King of a region that has no interest in being part of the Kingdoms, besides being her nephew.
Jaime killed her father, yes. But she is now quite aware of what her father was and she values Tyrion who is only alive because Jaime freed him. So I frankly don't see why Jaime is more "bollock" than any other option.

Jon is the only one with his own power block already in the show, that is certain.
But circumstances are likely to change quickly. If Jaime kills Cersei for example as many suspect he will; who is then in charge? Well by the same principles as Cersei's own power grab, Jaime is, because he is her closest relative, and because he killed her and took the throne knowing that not doing so would create a power vacuum.
Alternately Jaime may simply become Lord of the Westerlands, with an ally in Bronn who is given the Twins. Fed up with Cersei, he may marry Dany and switch sides.
So there are ways Jaime could become a powerful player in his own right very quickly, making him a logical candidate for a political marriage.

If we are talking show, not books, only SR is a character that exists and is still alive. But yes, I forgot about him. I kinda feel like he is not going to survive LF's scheming though.
I also forgot the eunuchs, but while they are still men, they are also, like Yara, incapable of producing heirs so useless for political marriage.
I also forgot Bran. That is actually a real possibility. There is no reason to believe he can't reproduce. I'm pretty sure he is in love with Meera though.

The show has a much narrower range of options for Dany to be sure. Based on the books I had a number of ideas, but they don't seem to really work in the show.
Available Male Characters (female + female does not produce heirs and is therefore useless for political marriage) in no particular order:
Tyrion (still somewhat married to Sansa so maybe not really available. ATM this marriage wouldn't help her cause).
Euron (no way in hell unless he finds a way to "capture" her, which would take serious magical help).
Jaime (He is no longer KG and is free to marry, so a definite possibility if she gets over him killing her father and he acquires some power to bargain with).
Sam (Gilly would have to be dead, and Sam would have to find himself with some serious power; maybe not just Horn Hill, but all of the Reach...and why not, since the Tyrells are dead).
Gendry (A decent way to bring together the Baratheon and Targ dynasties, but Gendry has some climbing to do before this would make any sense).
Jon (He is her nephew, so ew, but other than that it looks like a serious possibility).
Littlefinger (That would be some story, wonder how he would pull it off).
Tormund Giantsbane (Brienne is more his type, but would be one way to marry the Northern power block without marrying Jon).
Davos (Isn't he married?).
Bronn (I doubt Tyrion would advise this course, much as he likes Bronn).
Am I missing anyone?

There ARE no Baratheons.
Stannis is dead, Renly is dead, Shireen is dead. Gendry is supposed to be dead along with almost all of his known half-siblings. The only exceptions are Edric Storm and Mya Stone, both kept safe from the death order by competing powers, and in any case, they are bastards. The only one of these who was even acknowloedged by Robert is Edric, and he is a child in exhile with no means to gather support. Gendry and Mya would not even be able to prove their relationship to Robert and have no interest in doing so or in ruling.
What Baratheons are you thinking are going to appear out of the woodwork here? There simply are none.
Dany's claim is based in a dynasty that was overthrown. To stake her claim she has to reconquer. She has absolutely no Baratheon dynastic claim, and those with a stake in the current order are not going to just hand her the throne.

You need to reframe things in your head, starting with the question of who would have a better claim now that Tommen is dead without heirs.
Noone with a stake in the current order is going to be looking back to the overthrown Targ dynasty. And the Baratheons are all dead with the exception of a few lingering bastards.
Cersei is Tommen's closest living relative, and, more importantly, she moved fast to stake her claim, daring anyone to dispute her.

The basis is conquest. Her opponents are dead. She crowned herself before anyone could dispute the idea. Now anyone who doesn't like it will have to fight her, and most of her remaining opposition is in no position to do so.
The claim that there is some kind of legal versus illegal conquest is simply ridiculous. Conquest is killing your enrmies and taking what is not yours. Legality questions are a means of preserving peace when rulers die, but if people do not follow those rules and instead choose war, there is not a thing in the world that pieces of paper can do to prevent someone from grabbing power.

You apparently don't understand the most basic things about power and about what this series is about. Stannis had the right, and look how that went.
Sure, there are very likely many many people who will not be happy with Cersei grabbing the throne, for a large number of reasons.
It simply doesn't change anything about the reality of the situation. Cersei took the throne. She is daring anyone to defy her. No doubt some will, but others are terrified of her and in no shape to wage war. We will see if she is able to consolidate power or not, with fear being her only real tool for doing so, but at no point will paper heredity laws convince Cersei to step down, or people to stop fearing her.